In figureREF  3 communities are produced using
the Barabási–Albert model [1]}, [2]} algorithm of preferential attachment and then these communities
are connected by choosing nodes uniformly from each group.
The same format as with the previous figure is used. In the first row of subplots, a) and b), we can see again that there is a wider
distribution in the scores for the nodes with the BVA algorithm on non-boundary nodes.
In subfigures c) and d) we visualise the networks with the nodes scaled according to the BVA and betweenness respectively.
We can see that the highest degree nodes
which are central to the community they belong to are scaled and highlighted in both cases.
A critical difference
is that the boundary nodes at the top which receive a large score with BVA but are given minimal importance
with betweenness. With betweenness the role of these nodes is redundant given alternative routes through nodes with higher
degree and direct connections to many nodes in the community.
In the effort to inspire cross pollination of communities with promoted content, the ability to saturate a user
with fewer connections may be advantageous, and worth considering because they may be influenced more easily.
In e) we look at the overlap proportion of the ranking between nodes for a number of nodes in both algorithms.
We can see the local peak of the number of
overlaps for more nodes than the number of boundary nodes. This is because the structure of the network includes
nodes in the vicinity of the boundary which lay on the shortest paths to other nodes in the community.
In the last subfigure we can see the scatter plot of the BVA values and betweenness. The ranking of the algorithms may
be more similar to each other than with the ER communities connected but the distribution is much more narrow for betweenness
in this case, highlighting the few boundary nodes that are also core to the communities.
